set and multiset

Associative Container

An Associative Container is a variable-sized Container that supports efficient retrieval of elements (values) based on keys. It supports insertion and removal of elements, but differs from a Sequence in that it does not provide a mechanism for inserting an element at a specific position. [1]

As with all containers, the elements in an Associative Container are of type value_type. Additionally, each element in an Associative Container has a key, of type key_type. In some Associative Containers, Simple Associative Containers, the value_type and key_type are the same: elements are their own keys. In others, the key is some specific part of the value. Since elements are stored according to their keys, it is essential that the key associated with each element is immutable. In Simple Associative Containers this means that the elements themselves are immutable, while in other types of Associative Containers, such as Pair Associative Containers, the elements themselves are mutable but the part of an element that is its key cannot be modified. This means that an Associative Container's value type is not Assignable.

The fact that the value type of an Associative Container is not Assignable has an important consequence: associative containers cannot have mutable iterators. This is simply because a mutable iterator (as defined in the Trivial Iterator requirements) must allow assignment. That is, if i is a mutable iterator and t is an object of i's value type, then *i = t must be a valid expression.

In Simple Associative Containers, where the elements are the keys, the elements are completely immutable; the nested types iterator and const_iterator are therefore the same. Other types of associative containers, however, do have mutable elements, and do provide iterators through which elements can be modified. Pair Associative Containers, for example, have two different nested types iterator and const_iterator. Even in this case, iterator is not a mutable iterator: as explained above, it does not provide the expression *i = t. It is, however, possible to modify an element through such an iterator: if, for example, i is of type map<int, double>, then (*i).second = 3 is a valid expression.

In some associative containers, Unique Associative Containers, it is guaranteed that no two elements have the same key. [2] In other associative containers, Multiple Associative Containers, multiple elements with the same key are permitted.

set<Key, Compare, Alloc>

Set is a Sorted Associative Container that stores objects of type Key. Set is a Simple Associative Container, meaning that its value type, as well as its key type, is Key. It is also a Unique Associative Container, meaning that no two elements are the same.

Set and multiset are particularly well suited to the set algorithms includes, set_union, set_intersection, set_difference, and set_symmetric_difference. The reason for this is twofold. First, the set algorithms require their arguments to be sorted ranges, and, since set and multiset are Sorted Associative Containers, their elements are always sorted in ascending order. Second, the output range of these algorithms is always sorted, and inserting a sorted range into a set or multiset is a fast operation: the Unique Sorted Associative Container and Multiple Sorted Associative Container requirements guarantee that inserting a range takes only linear time if the range is already sorted.

Set has the important property that inserting a new element into a set does not invalidate iterators that point to existing elements. Erasing an element from a set also does not invalidate any iterators, except, of course, for iterators that actually point to the element that is being erased.

Multiset is a Sorted Associative Container that stores objects of type Key. Multiset is a Simple Associative Container, meaning that its value type, as well as its key type, is Key. It is also a Multiple Associative Container, meaning that two or more elements may be identical.